How to make a Stone/Clay Material?
Try using textures to add some subtle displacement and/or normal mapping. Box mapped image textures or procedural textures are perfect for this. For example, here's a simple procedural texture consisting of some high frequency details mixed with a few larger features, normal mapped onto a diffuse shader (plus a touch of displacement):







It may be helpful to throw in some image textures to get some more irregular larger-scale features.

Note that true displacement is required to get those tasty bits of self-shadowing near the terminators prevalent in your example. Displacement is still currently an experimental feature, so to use it you'll have to switch enable experimental features in Properties > Render > Feature Set. Once that's done, be sure to set the displacement method to True in the material settings.

Displacement means the actual geometry is being displaced, so for it to work you need a sufficiently dense mesh. Adaptive subdivision is ideal for this; to enable it, add a subsurf modifier and enable Adaptive under Render.

See Blender Cycles True Displacement for more details.



Also keep in mind that lighting is just as (or perhaps even more) important as the material itself. Part of what makes your example distinctive is the long light-to-shadow transitions which show off the fine details of the material.

Try playing around with lights and different lighting setups while making the material to get a sense of how it behaves under different conditions.